Question

What is the sum of the geometric sequence 1, 3, 9, ... if there are 11 terms? (5 points) 29,524 55,987 87,381 88,573

Answer 1

S₁₁ = 88573

Explanation:

the sum to n terms of a geometric sequence is

`S_(n)` =
`(a_(1)(r^(n)-1) )/(r-1)`

where a₁ is the first term and r the common ratio

here a₁ = 1 and r =
`(a_(2) )/(a_(1) )` =
`(3)/(1)` = 3 , then

S₁₁ =
`(1(3^(11)-1) )/(3-1)` =
`(1)/(2)` (177147 - 1) =
`(1)/(2)` × 177146 = 88573